Dissertations / Theses on the topic 'Vibrating gyroscope'
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Cruickshank, Jane Laura. "A vibrating silicon diaphragm micro gyroscope." Thesis, University of Newcastle Upon Tyne, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.285737.
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Avanesian, David. "HARDWARE IMPLEMENTATION OF ACTIVE DISTURBANCE REJECTION CONTROL FOR VIBRATING BEAM GYROSCOPE." Cleveland State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=csu1200587118.
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Gallacher, Barry J. "The design, fabrication and testing of a multi-axis vibrating ring gyroscope." Thesis, University of Newcastle Upon Tyne, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.413139.
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Tydor, Maximilián. "Univerzální senzorová testovací platforma." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2015. http://www.nusl.cz/ntk/nusl-221234.
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This document deals with issues of testing semiconductor inertial sensors like gyroscopes and accelerometers, but also other sensors like magnetometers, inclinometers and others for aviation navigation purposes where strict requirements cover every system. The goal of this thesis is to create modular test platform for testing wide variety of sensors in different combinations under variable circumstances. The development covers mechanical design, electrical design – hardware and also control algorithm – software.
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Zaman, Mohammad Faisal. "Degree-per-hour mode-matched micromachined silicon vibratory gyroscopes." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/28168.
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Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2008.Committee Chair: Dr. Farrokh Ayazi; Committee Member: Dr. Mark G. Allen; Committee Member: Dr. Oliver Brand; Committee Member: Dr. Paul A. Kohl; Committee Member: Dr. Thomas E. Michaels.
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Spelsberg-Korspeter, Gottfried [Verfasser]. "Self-excited vibrations in gyroscopic systems / Gottfried Spelsberg-Korspeter." Aachen : Shaker, 2007. http://d-nb.info/1164340719/34.
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White, Robert D. (Robert David) 1976. "Effects of impact and vibration on the performance of a micromachined tuning fork gyroscope." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/16723.
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Thesis (S.B. and S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999.Includes bibliographical references (p. 188).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
by Robert D. White.
S.B.and S.M.
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Gavrilovic, Nenad. "VIBRATION-BASED HEALTH MONITORING OF ROTATING SYSTEMS WITH GYROSCOPIC EFFECT." DigitalCommons@CalPoly, 2015. https://digitalcommons.calpoly.edu/theses/1358.
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This thesis focuses on the simulation of the gyroscopic effect using the software MSC Adams. A simple shaft-disk system was created and parameter of the sys-tem were changed in order to study the influence of the gyroscopic effect. It was shown that an increasing bearing stiffness reduces the precession motion. Fur-thermore, it was shown that the gyroscopic effect vanishes if the disk of system is placed symmetrically on the shaft, which reduces the system to a Jeffcott-Ro-tor. The second objective of this study was to analyze different defects in a simple fixed axis gear set. In particular, a cracked shaft, a cracked pinion and a chipped pinion as well as a healthy gear system were created and tested in Adams. The contact force between the two gears was monitored and the 2D and 3D frequency spectrum, as well as the Wavelet Transform, were plotted in order to compare the individual defects. It was shown that the Wavelet Transform is a powerful tool, capable of identifying a cracked gear with a non-constant speed. The last part of this study included fault detection with statistical methods as well as with the Sideband Energy Ratio (SER). The time domain signal of the individual faults were used to compare the mean, the standard deviation and the root mean square. Furthermore, the noise profile in the frequency spectrum was tracked with statistical methods using the mean and the standard deviation. It was demonstrated that it is possible to identify a cracked gear, as well as a chipped gear, with statistical methods. However, a cracked shaft could not be identified. The results also show that SER was only capable to identify major defects in a gear system such as a chipped tooth.
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Ling-Fang, Yao. "Design and analysis of a resonant gyroscope suitable for fabricaton using the LIGA process." Thesis, De Montfort University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.391334.
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Петренко, Олексій Володимирович. "Удосконалення методів підвищення точності вібраційного гіроскопа з металевим циліндричним резонатором." Thesis, КПІ ім. Ігоря Сікорського, 2020. https://ela.kpi.ua/handle/123456789/36992.
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Робота виконана на кафедрі аерокосмічних систем управління Національного авіаційного університету Міністерства освіти і науки України та у Публічному акціонерному товаристві «Науково-виробниче об’єднання «Київський завод автоматики».Дисертаційна робота присвячена науковому обґрунтуванню та розробці алгоритмів компенсації внутрішніх похибок та зовнішніх збурень у Коріолісовому вібраційному гіроскопі, а також удосконаленню його складових частин (резонатора, чутливого елементу). Автором розроблено методику та обладнання для робочого місця безелектродного вимірювання динамічних параметрів металевого резонатора після його виготовлення, розроблено конструкцію приладдя для приклеювання п’єзоелектродів до резонатора нової конструкції, методику та обладнання робочого місця для балансування мас. Розроблено та відпрацьовано на експериментальному зразку КВГ методики температурної корекції фаз сигналів квадратури та кутової швидкості, багатопараметричної корекції дрейфу нуля і масштабного коефіцієнту, що призводить до збільшення точності виміру кутової швидкості в умовах дії температурних градієнтів.
In the thesis the following new scientific results are obtained: 1. For the first time, a multi-parameter method of CVG scale factor correction is developed and implemented, which can be used during the CVG operation in the rate and in the differential modes. Ukraine patent have been obtained for this method. 2. Scientifically grounded analysis of a new design of a cylindrical resonator with holes on the walls of a cylinder having higher vibration resistance was first developed and carried out. 3. The multiparameter bias correction algorithm has been developed and implemented, which has advantages over the existing ones by accuracy. 4. For the first time experimental researches were carried out on a manufactured experimental sample of CVG with developed metal cylindrical resonator made of elenvar elloy, which showed high accuracy scale factor and bias drift correction under the action of temperature gradient, as well as high shockvibration resistance of the sample. The practical significance of thesis results are: − comparison of two designs of metallic cylindrical resonators with holes on the bottom and on the wall of the cylinder and by calculations and computer simulation the advantages of the second design over the first one in the part of shock resistance have been substantiated; − аn analysis of the different geometries of the holes has been made. Their influence on the resonant oscillation frequencies of a cylindrical resonator is revealed. Recommendations for the geometry of the resonator and its elements have been developed; − improved design of the base on which the newly designed resonator with holes on the wall of the cylinder is installed; − the choice of electrodes used for oscillation excitation and measurement of the signals is experimentally substantiated; − the technique and equipment for workplace electrodeless measurement of metallic resonator dynamic parameters after its manufacture have been developed; − the influence of frequency mismatch, wave angle and positioning errors of the electrodes on the CVG bias and scale coefficient have been evaluated; − a new accessory design has been developed to attach the electrodes to the new resonator design; − the technique and equipment of the workplace for balancing the mass of the resonator on the fourth harmonic of the unbalance to reduce its frequency mismatch have been developed. The technique was tested in the manufactured ample of CVG; − the technique of measuring the angles of non-orthogonality of the sensitive axis to its mounting surface has been developed and implemented in the experimental sample of CVG; − the use of CVG to improve the accuracy of armament stabilization was analyzed; − improved CVG standing wave control algorithm block diagram, which provides a fast start of the gyroscope when it is turned on at any temperature in the range of operating temperatures; − the techniques for temperature correction of quadrature and angular rate phases, multiparameter correction of CVG bias and scale factor have been developed and tested on experimental sample of CVG, which leads to an increase in the accuracy of measuring angular rate under temperature gradients; − the experimental results showed that the CVG with a metallic resonator is resistant to multiple shocks with amplitude 100 g and its bias is slightly dependent on the shock amplitude and does not exceed 5×10−3 deg/s. The bias sensitivity to vibration perturbations is 2.5×10−3 deg/s/g.
Диссертация посвящена научному обоснованию и разработке алгоритмов компенсации внутренних погрешностей и внешних возмущений в Кориолисового вибрационном гироскопе, а также совершенствованию его составных частей (резонатора, чувствительного элемента). Автором разработана методика и оборудование для рабочего места безэлектродного измерения динамических параметров металлического резонатора после его изготовления, разработана конструкция приспособления для приклеивания пьезоэлектродов к резонатору новой конструкции, методику и оборудование рабочего места для балансировки масс резонатора. Разработано и отработано на экспериментальном образце КВГ методики температурной коррекции фаз сигналов квадратуры и угловой скорости, многопараметрической коррекции дрейфа нуля и масштабного коэффициента, что приводит к увеличению точности измерения угловой скорости в условиях действия температурных градиентов.
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Chowdhury, Sanjib. "Effect of Shaft Vibration on the Dynamics of Gear and Belt Drives." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1267990279.
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Lu, Haohui. "Vibration Properties and High Speed Stability of a Rotating Piezoelectric Energy Harvesting Device That Experiences Gyroscopic Effects." OpenSIUC, 2016. https://opensiuc.lib.siu.edu/theses/2050.
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This study investigates the vibration of a rotating piezoelectric device that consists of a proof mass that is supported by elastic structures with piezoelectric layers. Vibration of the proof mass causes deformation in the piezoelectric structures and voltages to power electrical loads. The coupled electromechanical equations of motion are derived using Newtonian mechanics and Krichhoff's circuit laws. The free vibration behavior is investigated for devices with identical (tuned) and nonidentical (mistuned) piezoelectric support structures and electrical loads. These devices complex-valued have speed-dependent eigenvalues and eigenvectors as a result of their constant rotation. The imaginary parts of the eigenvalues physically represent the oscillation frequencies of the device. The real parts represent the decay or growth rates of the oscillations, depending on their sign. The complex-valued components of the eigenvectors physically represent the amplitudes and phases of the vibration. The eigenvalue behaviors differ for tuned and mistuned devices. Due to gyroscopic effects, the proof mass in the tuned device only vibrates in either forward or backward decaying circular orbits in single-mode free response. This is proven analytically for all tuned devices. For mistuned devices, the proof mass has decaying elliptical forward and backward orbits. The eigenvalues are shown to be sensitive to changes in the electric load resistances. Closed-form solutions for the eigenvalues are derived for open and close circuits. At high rotation speeds these devices experience critical speeds and instability. Closed-form solutions for the critical speeds are derived. Tuned devices have one degenerate critical speed that separates stable speeds from unstable speeds, where flutter instability occurs. Mistuned devices have two critical speeds. The first critical speed separates stable speeds from speeds where divergence instability occurs. Divergence instability continues for small speeds above the second critical speed. At higher supercritical speeds flutter instability occurs. Transitions between stable and unstable eigenvalues are investigated using root locus diagram. This device has atypical eigenvalue behavior near the critical speeds and stability transitions compared to conventional gyroscopic systems.
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Tran, Thang Quang. "DYNAMIC RESPONSE OF AND POWER HARVESTED BY ROTATING PIEZOELECTRIC VIBRATION ENERGY HARVESTERS THAT EXPERIENCE GYROSCOPIC EFFECTS." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/theses/2157.
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This study investigates energy harvesting characteristics from a spinning device that consists of a proof mass that is supported by two orthogonal elastic structures with the piezoelectric material. Deformation in the piezoelectric structures due to vibration of the proof mass generates voltages to power electrical loads. The governing equations for this electromechanically coupled device are derived using Newtonian mechanics and Kirchhoff's voltage law. The case where the device rotates at a constant speed and is subjected to sinusoidal base excitation is examined in detail. The energy harvesting behavior is investigated for devices with identical piezoelectric support structures (called tuned devices). Closed-form expressions are derived for the steady state response and power harvested. For nonzero rotation speeds, these devices have multifrequency dynamic response and power harvested due to the combined vibration and rotation of the host system. The average power harvested for one oscillation cycle is calculated for a wide range of operating conditions to quantify the devices' performance. Resonances do not occur for cases when the base excitation frequency is fixed and the rotation speed varies. For cases of fixed rotation speed and varying base excitation frequency, however, resonances do occur. The number and location of these resonances depend on the electrical circuit resistances and rotation speed. Resonances do not occur at speeds or frequencies predicted by resonance diagrams, which are commonly used in the study of rotating system vibration. These devices have broadband speed energy harvesting ability. They perform equally well at high and low speeds; high speeds are not necessary for their optimal performance. The impact of the chosen damping model on energy harvesting characteristics for tuned devices is investigated. Two common damping models are considered: viscous damping and structural (hysteretic) damping. Closed-form expressions for steady state dynamic response and power harvested are derived for models with viscous and structural damping. The average power harvested using the model with structural damping behaves similarly at high speeds and low speeds, and at high resistances and low resistances. For the viscous damping model, however, the average power harvested is meaningfully different at high speeds compared to low speeds, and at high resistances compared to low resistances. The characteristics of devices with nonidentical piezoelectric support structures (called mistuned devices) are investigated numerically. Similar to spinning tuned devices, mistuned devices have multifrequency dynamic response and power harvested. In contrast to tuned devices, high amplitude average power harvested occurs near speeds and base excitation frequencies predicted by resonance diagram.
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Cooley, Christopher Gary. "High-Speed Dynamics and Vibration of Planetary Gears, Vibration of Spinning Cantilevered Beams, and An Efficient Computational Method for Gear Dynamics." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1354558979.
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Pham, Hai Minh. "Computation of the vibration of a whole aero-engine model with nonlinear bearings." Thesis, University of Manchester, 2010. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:128171.
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Aero-engine assemblies are complex structures typically involving two or three nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. The deployment of SFDs into such structures is highly cost-effective but requires careful calculation since they can be highly nonlinear in their performance, particularly if they are unsupported (i.e. without a retainer spring). The direct study of whole-engine models with nonlinear bearings has been severely limited by the fact that current nonlinear computational techniques are not well-suited for complex large-order systems. The main contributions of this thesis are: • A procedure for unbalance response computation, suitable for generic whole-engine models with nonlinear bearings, which significantly extends the capability of current finite element packages. This comprises two novel nonlinear computational techniques: an implicit time domain integator referred to as the Impulsive Receptance Method (IRM) that enables rapid computation in the time domain; a whole-engine Receptance Harmonic Balance Method (RHBM) for rapid calculation of the periodic response in the frequency domain. Both methods use modal data calculated from a one-off analysis of the linear part of the engine at zero speed.• First-ever analyses on real twin-spool and three-spool engines. These studies illustrate the practical use of these solvers, provide an insight into the nonlinear dynamics of whole-engines and correlate with a limited amount of industrial experimental data. Both IRM and RHBM are directly formulated in terms of the relative response at the terminals of the nonlinear bearings. This makes them practically immune to the number of modes that need to be included, which runs into several hundreds for a typical engine. The two solvers are extensively tested on two/three-shaft engine models (with 5-6 SFDs) provided by a leading engine manufacturer using an SFD model that is used in industry. The tests show the IRM to be many times faster than an established robust conventional implicit integrator while achieving a similar level of accuracy. It is also shown to be more reliable than another popular implicit algorithm. The RHBM enables, for the first time, the frequency domain computation of the nonlinear response of whole-engine models. Its use is illustrated for both Single-Frequency Unbalance (SFU) excitation (unbalance confined to only one shaft) and Multi-Frequency Unbalance (MFU) excitation (unbalance located on two or more shafts, rotating at different speeds). Excellent correlation is demonstrated between RHBM and IRM.The parametric studies compare and contrast the frequency spectra for SFU and MFU cases. They also reveal the varying degree of lift at the unsupported SFDs. The sensitivity of the response to end-sealing and bearing housing alignment is also illustrated. It is demonstrated that the use of suitably preloaded vertically oriented “bump-springs” at the SFDs of heavy rotors produces a significant improvement in journal lift. It is also shown that the consideration of a slight amount of distributed damping in the structure significantly affects the predicted casing vibration levels, bringing them closer to measured levels, while having little effect on the SFD orbits.
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Hurel, Gabriel. "Simulation du comportement vibratoire non linéaire induit par frottement des freins aéronautiques." Thesis, Ecully, Ecole centrale de Lyon, 2014. http://www.theses.fr/2014ECDL0016.
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Le présent document a pour objet la modélisation transitoire non linéaire du comportement vibratoire des systèmes de frein aéronautiques. Le but est de reproduire numériquement l’apparition et le niveau des vibrations au cours du temps, afin de les maîtriser et d’adapter la conception du frein. Les essais de freinage mettent en évidence deux modes de vibration que sont le whirl et le squeal. Si les niveaux de ces vibrations deviennent trop importants, la structure de la roue et du train d’atterrissage peut être endommagée. Afin d’éviter de tels dommages, la conception du frein doit être adaptée. Pour réaliser cela, Messier-Bugatti-Dowty doit disposer d’un modèle capable de prédire les niveaux de vibration du frein au cours du temps pendant la phase de freinage. Le modèle doit avoir une précision suffisante, être en lien avec la maquette numérique et ne doit pas exiger de recalage. Un premier travail vise à améliorer le modèle éléments finis existant qui se révèle être trop imprécis. Une étude portant sur les effets gyroscopiques permet d’évaluer leur impact sur la fréquence et la stabilité des modes de whirl. Une modélisation plus complète du bâti d’essai améliore la précision de la fréquence du mode de squeal. Enfin, le mode de whirl est mieux simulé grâce au développement d’un modèle de pneumatique à partir de son analyse modale. Ce modèle est ensuite réduit afin de réaliser une intégration temporelle. Une sous-structuration permet de séparer l’ensemble des disques du frein, où le frottement et la non-linéarité se situent, du reste de la structure considérée comme linéaire. Trois techniques de réduction de l’ensemble des disques sont exposées. On évalue leur représentativité par rapport au modèle non-réduit en comparant les fréquences et la stabilité des modes propres. La première méthode est une représentation nodale de l’ensemble des disques. Les équations décrivant la non-linéarité et le frottement sont analytiques. Pour la deuxième méthode, la non-linéarité est déplacée à l’extrémité de l’ensemble des disques pour la découpler du frottement. La troisième méthode, plus ambitieuse et complexe, conserve à la fois l’emplacement de la nonlinéarité aux interfaces frottantes et la géométrie des disques. Une technique de réduction modale permet d’abaisser le nombre de degrés de liberté non linéaires. Pour clore ce rapport, des simulations transitoires sont calculées à partir des modèles réduits. Des études d’influences sont réalisées. Les paramètres étudiés sont le type d’algorithme d’intégration temporelle, l’amortissement introduit, la loi non linéaire, la pression hydraulique d’entrée et le coefficient de frottement. Leurs impacts sur les niveaux et la durée d’apparition des vibrations est évaluéThis report deals with the non-linear transient simulation of the dynamic behaviour of aeronautic brake systems. The objective is to reproduce the occurrence and level of vibrations versus time in order to control and adjust design consequently. The braking tests highlight two eigenmodes, which are called whirl and squeal. If the level of these vibrations becomes too high, the structures of the wheel and the landing gear may be damaged. To avoid damage, the design has to be adjusted. To achieve this, Messier-Bugatti-Dowty requires a model that is able to predict the levels of vibrations of the brake when it is braking. This model must have an adequate accuracy, be linked to the digital mockup and not require tuning. First, the existing finite element model has to be improved because its initial accuracy is not acceptable. A study about gyroscopic effects allows to assess their impact on the frequency and the stability of whirl modes. A complete modelling of the test frame improves the squeal modes’ frequency accuracy. At last, the whirl modes are better simulated due to the development of a tyre model based on modal analysis data. Then, the finite element model is reduced in order to perform a temporal integration. A substructuring allows to separate the set of brake discs (heat sink), where friction and non-linearities are located, from the rest of the structure which is considered linear. Three heat sink reduction techniques are proposed. Their representativeness are estimated compared to the non-reduced model. The first technique is a nodal description of the heat sink. The equations of friction and non-linearity are analytical. For the second technique, the non-linearity is displaced to the extremity of the heat sink to uncouple it from friction. The third technique, more ambitious and complex, keeps the location and non-linearity in friction interfaces and discs geometry. A reduction technique enables to decrease the number of non-linear degrees of freedom. As a conclusion, transient simulations are computed from reduced models. Sensitivity studies are performed. Studied parameters are the type of integration solver, introduced damping, non-linearities, hydraulic pressure, and friction coefficient. Their impacts on level and duration of occurrence of vibrations is estimated
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Vu, Trong Dai. "Modélisation des effets tournants du pneumatique et des forces decontact pour le bruit de roulement basses fréquences." Thesis, Paris Est, 2014. http://www.theses.fr/2014PEST1051/document.
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Le bruit de roulement contribue fortement au bruit perçu à l'intérieur de l'habitacle des automobiles. Ce bruit a pour origine le contact du pneumatique sur une chaussée rugueuse. En basses fréquences (0-400 Hz), il est transmis dans l'habitacle du véhicule essentiellement par la voie solidienne. La méthode actuelle de prévision de ce bruit chez PSA Peugeot Citroën repose sur une approche mixte calcul-mesure longue, coûteuse et pas suffisamment prédictive. Pour contourner ces limitations, une filière purement numérique est envisagée. Elle demande de modéliser le comportement vibro-acoustique du pneumatique en prenant en compte les effets liés à la rotation et de résoudre le problème de contact avec une chaussée rugueuse. Concernant la modélisation d'un pneumatique en rotation, des formulations des effets tournants d'un solide déformable sont établies en utilisant une approche Arbitrairement Lagrangienne Eulérienne (ALE). Ces formulations sont validées par une application sur un nouveau modèle simplifié du pneumatique. Il s'agit d'un modèle d'anneau circulaire incluant les effets de cisaillement soumis localement à une charge représentative de la masse du véhicule. Un modèle plus complexe d'ensemble monté pneu/roue/cavité intégrant l'ensemble des effets liés à la rotation est également validé par une comparaison avec des essais. Ensuite, le contact avec une chaussée réelle est formulé par différentes approches permettant de réduire le temps de calcul pour une utilisation industrielle. En particulier, le calcul du contact est décomposé en un calcul statique non linéaire suivi d'un calcul dynamique linéaire. La validation du modèle de contact est réalisée par une comparaison calcul/essai. Les résultats sont très satisfaisantsThe rolling noise contributes significantly to the noise inside cars. This noise comes from the tire/road contact. In low frequencies (0-400 Hz), it is mainly transmitted into the cabin through structural vibration. The current method used at PSA Peugeot Citroen to predict this noise, is a mixed simulation/experimental approach which is long, expensive and not sufficiently predictive. In order to overcome these difficult, a full numerical approach is considered. It requires modeling the tire vibration by taking into account the rotating effects and the contact with the rough surface. Concerning the model of rotating tire, a formulation of a deformable solid is constructed by using an Arbitrary Lagrangian Eulerian approach (ALE). This formulation is validated by an application on a new simplified tire model which is a circular ring including the shear stresses and the non linear effects due to the vehicle weight. A more complex model composed of tire/wheel/cavity including all the rotating effects is also validated by comparison with experiments. Then the contact with a real road is calculated by different approaches to get the acceptable computing time for industrial uses. In particular, the calculation of the contact is divided into a non-linear static analysis followed by a linear dynamic calculation. The validation of this model is successfully achieved by comparison test results
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Yang, Wen-Chang, and 楊文彰. "Vibrating analysis of silicon ring-type micro gyroscope." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/48143083741764866019.
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Tsai, Chi-Yang, and 蔡奇洋. "Micro Vibrating Ring Gyroscope Fabricated with Fusion Bonding." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/96882589889542767171.
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Chuo, Tang Chuan, and 周唐詮. "Fabrication for the Structure of Micro-Vibrating Ring Gyroscope." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/77641725005099044488.
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碩士國立交通大學
機械工程系
90
The main purpose of this thesis is to fabricate the structure of vibrating ring gyroscope based on MEMS technology by replacing the conventional mechanical gyroscopes with high cost, and complication as well as uneasily-fabricate. The vibrating ring gyroscope in this thesis is one kind of vibrating shell gyroscopes. By means of VLSI and micromachined techniques, we can realize the fabrication of main structure with small size and decrease fabrication cost on batch process. In this thesis, we use lithography, anodic bonding, wet etching (KOH), and dry etching (ICP or RIE) to implement our micro-vibrating structure.
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Wang, Yu-Bin, and 王毓斌. "Study for Fabricating an Anisotropic Silicon Ring Vibrating Gyroscope." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/14290612288551138420.
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碩士國立臺灣大學
應用力學研究所
95
This thesis presents the fabrication of a 150um tall (100) single-crystal silicon ring gyroscope with high aspect-ratio fabricated by MEMS technology. A new design of vibrating ring will be introduced to ensure the resonance frequency of both and molds being the same. Four kinds of support springs are designed and put into experiment to find out the best one. All the recipes and methods for the MEMS processes in this experiment will be described, such as BOE wet etch, ICP dry etch, photolithography, anodic bonding, and metallization.
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Shieh, Fa-Hwa, and 謝發華. "Theory and Error Analysis of a Vibrating Hemispherical Gyroscope." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/26950501334983158397.
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博士國立臺灣大學
應用力學研究所
89
The paper considers the theory of a new type of vibrating hemispherical gyroscope, which comprises a hemispherical shell with discrete piezoceramic actuation and sensing elements bonded on the outer side and close rim of the shell. Constitutive equations for a thin piezoceramic shell with thickness polarization and electrode-covered faces are derived using Niordson’s shell theory. Coupled electromechanical equations of motion, describing the dynamics of the vibrating hemispherical gyroscope, are derived using Hamilton’s principle, Lord Rayleigh’s solution of the shell and Rayleigh-Ritz method. The linear error model due to imperfections of materials or manufactural of tolorance of vibrating gyroscopes is established. The operation of the gyroscope without and with imperfections are described under free vibration. The equation of motion of two operation modes of vibrating gyroscopes, whole-angle-tracking and forced-to-balance modes, are derived.
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Lu, Kun-Hua, and 呂昆樺. "The Design of Sensing Circuit for Micro-Vibrating Ring Gyroscope." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/29496685307593988631.
Full textAbstract:
碩士國立交通大學
機械工程系所
93
Probing into design of the capacitance detecting circuit for the micro gyroscope is the purpose of this thesis. Micro gyroscope is the small structure made with MEMS process. The sensing signal of this gyroscope due to the gap changes while the gyroscope shakes, then the capacitive value between the gap changes too. The capacitive value is very small and usually of fF grade. If we connect this signal to the sensing circuit on PCB, this signal can not be examined out because the signal/noise ratio is too small. So in this thesis, we try to design the capacitance detecting circuit in integrated circuit technology in order to reduce the noise of the sensing circuit. Presently, the popular method in capacitance detecting circuit contains of the synchronous detection circuit and the switched capacitor sensing circuit. The switched capacitor sensing circuit needs complicated clock circuits and suffers from the noise of the MOS switch. However, the synchronous detection circuit doesn’t. Besides, it can cancel the parasitic capacity and the 1/f noise. So we select the synchronous detection circuit for use. This thesis contains of examining circuit structure, circuit analysis, design, simulation and realization for the synchronous detection circuit with the model of TSMC 0.35um , 2P4M , Mixed-mode, 3.3, 5V.
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Lee, Hsin, and 李欣. "The Analysis and Design of The Micro Vibrating Ring Gyroscope." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/96690294361823460017.
Full textAbstract:
碩士國立交通大學
機械工程系
88
In this thesis, we analyzed this vibrating ring gyroscope using the finite element program ANSYS 5.3. The analyses we performed were divided mainly into three categories, the modal analysis, the static analysis and the thermal analysis. In the modal analysis, we obtained the two vibration flexural mode shapes, which is n=2, of this structure. We also obtained the frequencies of these two flexural modes. In the static analysis, we established the relations between the sensitivity of the structure and the geometry parameters including the width, the radius and the thickness. Besides, we also obtained the stress distribution of this structure and the ratio between the displacement along z-axis and the one along x or y-axis. In the thermal analysis, we discovered that the displacement of the structure due to thermal expansion is thousand times the one due to electrostatic force. To solve this problem, we designed a mechanism and changed the dimensions of the structure to decrease the displacement of the structure due to thermal expansion. Through these analyses, we designed the dimensions of this structure and changed the shape of the connection points between the ring and the spring to accomplish the demand of the analytical results.
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Chen, Jung-Chuan, and 陳嶸權. "Design and Fabrication of a Single-Crystal Micro Vibrating Ring Gyroscope." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/21795014378376337122.
Full textAbstract:
碩士國立清華大學
工程與系統科學系
90
The gyro is getting more important applications in many fields. A traditional gyro has some drawbacks, for example, they are bulky in volume and wear of bearings is not avoidable. However, the vibratory micro gyro can sense changes of angular velocity based on conservation of momentum and due to its simple and fixed structure the gyro doesn’t has the problem of wear. The vibratory gyro has long operating time. The size of a vibratory gyro is small so it has higher bandwidth and better linearity then those traditional gyro. This research is designed a two-dimensional vibratory micro-gyro which be driven by electro-static force, transduce angular velocity by capacitance. The micro gyro is fabricated by high aspect ratio micromachining process. According to the results of design, the gyro will be driven by electrostatic with 2.5 volts without vacuum. In the operating range of 0-200 deg/sec the sensitivity of gyro is 0.02 deg/secand the operation temperature range is -40℃-85℃. The size of fabricated device is 5mm×5mm×50um and structure of the gap is 3 um.
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Shen, Chia-Hao, and 沈家豪. "The analysis and optimal design of (100) silicon vibrating ring gyroscope." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/02336089062246984677.
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Huang, Chiou-An, and 黃秋安. "Compensation and Control Method for Micro-machined Axisymmetric Vibrating-shell Gyroscope." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/14378851781383097027.
Full textAbstract:
碩士國立臺灣大學
機械工程學研究所
87
Gyroscopes are rotation sensors. The axisymmetric vibrating-shell gyroscope can be used to measure not only the rotation rate but also the rotation angle. However, the restriction of the fabrication process may cause little asymmetry. In this thesis, we discuss the behavior of precession of node after compensating. Moreover, we study suitable control loops for different detecting method. Four balancing electrodes are used to compensate the asymmetry and the sensitivity method is used to calculate the balancing voltage. The precession rate of the node of asymmetry can be calculated by the numerical method. In the rate sensing modes, force-to-rebalance method performs better than the open-loop method in the aspects of response time and sensing linearity. In the control process, it is most important to get the natural frequency of the gyroscope. In this article, we adopt phase locked loop to lock the natural frequency. The phase locked loop works successfully for quality factor not larger than 2500.
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翁瑞鴻. "Investigation on the Hybrid Ring-type Vibrating Micro Gyroscope and Accelerometer." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/44270836517463519992.
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Chang, Cheng-Hui, and 張正輝. "The Dynamic Analysis of a Three-Axis Vibrating Micro-Ring Gyroscope Made of Si(100)." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/55960966256072146105.
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Ansari, Masoud. "Modeling and vibration analysis of a rocking–mass gyroscope system." Thesis, 2008. http://hdl.handle.net/10155/6.
Full textAbstract:
Rocking-mass gyroscope consists of an assembly of four cantilever beams with a rigid mass attached to them in the middle subjected to base rotations. Due to the gyroscope effect, the beams undergo coupled flexural-torsional vibrations. The main goal of the research is to develop an accurate model of such a system and along this line a detailed mathematical modeling of the gyroscope is developed. The equations of motion clearly show the presence of the gyroscopic couplings in all cantilever beams. A computer simulation model in its most general form has been developed, to analyze the effectiveness of this type of gyroscope.UOIT
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Ho, Cheng Yu, and 何承豫. "Design and Implementation of CMOS-MEMS Vibrating gyroscopes." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/66382812727352802936.
Full textAbstract:
碩士國立清華大學
動力機械工程學系
104
This study implements a MEMS gyroscope by TSMC 0.18μm 1P6M standard CMOS process. The structure which fabricates by this process must encounter the problem of residual stress warping. In order to reduce the deformation of the residual stress, this study integrates several structure design method in existing literatures. The design methods which be implemented in this research including symmetric stack structure and pure oxide structure are expected to achieve a structure of low residual stress warping. By this way, the fabrication parameter of this standard platform would not be modified to fit the demand of structure and the advantage of this platform would also be kept include monolithic integration capability and the good ability of electrical routing. However, for the gyroscope, the problem of low signal response may have chance to be compensated by the advantage of this platform which could make sub-micron sensing gaps.
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Chiou, Yen-Lin, and 邱彥霖. "Evaluation of structural vibration suppression using a gyroscope." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/84qscr.
Full textAbstract:
碩士國立臺灣大學
機械工程學研究所
105
Urbanization attracts people to cities and results in high population density. To provide enough living space for the residents, high-rise buildings are becoming increasing popular. A high-rise building suffers from the sway induced by wind and seismic activities and should be equipped with vibration suppression devices. Due to the gyroscopic effect, a high speed gyroscope can provide a strong reacting moment to resist the change of rotation direction due to external disturbances. As a consequence, a high speed gyroscope has the potential to be an effective device for the suppression of structure vibrations. This thesis aims to evaluate the ability of a gyroscope for structural vibration suppression. The gyroscope stands vertically in the undisturbed configuration, which coincides with the singular point of the conventional 3-2-3 Euler angles. To avoid this singularity, the 1-2-3 Euler angles are used to describe the configuration of the gyroscope. We first derive the transformation between these two sets of Euler angles and then discuss the effects of spin speed on the behavior of the gyroscope. This thesis discusses two simple structural models: one is a single floor model which is restricted to move in the horizontal plane; the other is a two-floor model which incorporates the bending deformation effects of a real structure. Lagrange equations are used to derive the governing equations of the structure-gyroscope system. The response of the structure with and without the gyroscope under impulsive and sinusoidal base excitations are determined via numerical integration. In this case, the effects of the spin rate of the gyroscope on the structure vibrations are investigated thoroughly.
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Cheng, I.-Chun, and 陳奕君. "Transduction and Compensation for Micro-machined Axis-symmetric Vibrating-shell Gyroscopes." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/27340703443645039834.
Full textAbstract:
碩士國立臺灣大學
機械工程學系研究所
86
Nowadays, the theories related to axis-symmetric vibrating-shell gyroscopes are quite complete and well established. In this article, we carry on theelopm ent of micro-machined axis-symmetric resonant gyroscope and focus on the drivi ng and sensing for it. Furthermore, we also discuss the behavior of thegyrosco pe due to little asymmetry and introduce the methods of compensation. As to th e functions, axis-symmetric resonant gyroscopes can be used to directlymeasure not only the rotation rate but also the rotation angle. In the ratesensing mo des, force-to-rebalance method performs better than the open-loopmethod in the aspects of response time and sensing linearity. Moreover, in thewhole angle m odes, the periodic excitation method is much more practicable thanthe impulse excitation method. Besides, whole angle modes are better than therate sensing modes because they can reduce the drift due to integration andavoid encounteri ng the restriction from sensing threshold. We adop the capacitivetype to excit e, sense and compensate. The capacitive sensor reveals severaladvantages, such as extremely high sensitivity, low power consumption, and bettertemperature p erformance. Combining the advantages mentioned above and high-Q propertyof the resonantor, the micro-machined axis-symmetric vibrating-shell gyroscopescan p erform quite well.
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Madeira, Bernardo Pereira. "Characterization of MEMS Coriolis Vibratory Gyroscopes." Master's thesis, 2021. http://hdl.handle.net/10362/125440.
Full textAbstract:
A MEMS Gyroscope is a micromachined inertial sensor that can measure the angle of
orientation or the angular rate of rotation. These devices have the potential to be used in
high precision navigation, safety and consumer electronics applications.
Due to their complexity, MEMS Gyroscopes are prone to have imperfections that
inhibit their full potential. By deeply characterizing these sensors, it is possible to validate
fabrication methodologies, apply control circuit mechanisms, and design alternative
mechanical structures that improve the performance.
In this project, a streamlined methodology for testing and characterizing these devices
is presented and executed. Analysis to the obtained results is given. Aditionally, a
prototype circuit was designed to operate the sensors in a closed-loop mode.
Two families of gyroscopes with different thickness were characterized - 40 m and
100 m. The devices presented low sensitivity thresholds due to the presence of a large
quadrature error. A phase sensitive demodulation solution was provided to eliminate
this noise source. The 40 m presented an overall better performance. A Python Script to
extract key noise performance parameters was also displayed.Giroscópios MEMS são micro sensores inerciais que conseguem medir o ângulo de orientação ou a variação ângular de uma rotação. Estes dispositivos têm o potencial de ser usados em aplicações de alta precisão para sistemas de navegação, segurança e para eletrónica comercial. Devido à sua complexidade, os Giroscópios MEMS são propensos a imperfeições que inibem o seu potencial máximo. Através da caracterização extensa destes sensores, é possível validar as metodologias de fabricação, aplicar circuitos de controlo e projetar estruturas mecânicas alternativas que melhorem a sua performance. Neste projeto é apresentada uma metodologia substanciada para testar e caracterizar estes dispositivos. Os resultados obtidos foram analisados. Adicionalmente, foi desenhado um protótipo de um circuito que opera os sensores em circuito fechado. Duas famílias de giroscópios com diferentes espessuras foram caracterizadas - 40 m e 100 m. Os dispositivos apresentaram baixos graus de sensibilidade devido a uma forte influência do erro de quadratura. Foi aplicada uma demodulação sensível à fase para melhoramento da performance. Um programa em Python para extrair parâmetros de ruído na resposta é apresentado.
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Wei-fan, Lai, and 賴威帆. "Theory and Analysis of a Three Dimensional Vibration Ring-Type Micro Gyroscope." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/83537943416574415289.
Full textAbstract:
碩士國立臺灣大學
應用力學研究所
91
This thesis mainly discuss about the theory and analysis of a vibrating ring-type gyroscope. At first, we use Hamilton’s principle to calculate the natural resonant frequencies and mode shapes of free vibration of a ring. We make the frequencies of in-plane and out-of-plane mode equal by designing the dimension of the ring. Next, we add 8 suspends into the ring and design the shape of a real micro gyroscope. We use Lagrange’s equation to derive the equations of motion and get some important parameters of a gyro, such as sensing coefficients. Finally, we select electrostatic actuators to excite the gyro into vibrating. We derive the complete equations of motion and use perturbation techniques to get the solutions. We also do numerical simulations at last.
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Tai-Wei, Lin. "Design of Kalman Filters for State Estimation of Piezoelectric Vibration Gyroscopes." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0005-2508200612402200.
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Lin, Tai-Wei, and 林泰瑋. "Design of Kalman Filters for State Estimation of Piezoelectric Vibration Gyroscopes." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/42582033396599788062.
Full textAbstract:
碩士國立中興大學
電機工程學系所
94
Standard Kalman filters (KF) and extended Kalman filters (EKF) have been commonly applied in the state estimation of maneuvering targets. Standard KFs minimize the estimated error variance between clean signal and its estimation. EKFs solve the weighted least-squares predictor-corrector feature for nonlinear stochastic systems. However, their performances might not be expected because the exact process noise covariance and measurement noise covariance are usually hard to achieve. We propose here a method for design of standard KFs and EKFs to estimate the angular velocity from a piezoelectric vibration gyroscope. In the proposed estimating scheme, a conventional KF combined with a double population genetic algorithm (DPGA) is first used to improve the estimation performance. Then, an EKF combines with DPGA is considered. The DPGA is used to determine the optimal process noise covariance during state estimation. Based on it a more accurate state estimation is shown to be achievable. Simulation results presented show that the gyroscope can accurately measure angular rate. Results of simulation and experimental verification are presented.
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Shi, Jian-Feng. "Embedded system software development for a single-gimbaled control moment gyroscope and the vibration damping of a clamped-free cantilevered beam." 2004. http://link.library.utoronto.ca/eir/EIRdetail.cfm?Resources__ID=94862&T=F.
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Åkerblom, Svensson Johan, and Carlsson Joakim Gullberg. "Analysis of comparative filter algorithm effect on an IMU." Thesis, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-54147.
Full textAbstract:
An IMU is a sensor with many differing use cases, it makes use of an accelerometer, gyroscope and sometimes a magnetometer. One of the biggest problems with IMU sensors is the effect vibrations can have on their data. The reason for this study is to find a solution to this problem by filtering the data. The tests for this study were conducted in cooperation with Husqvarna using two of their automowers. The tests were made by running the automowers across different surfaces and recording the IMU data. To find filters for the IMU data a comprehensive literature survey was conducted to find suitable methods to filter out vibrations. The two filters selected for further testing were the complementary filter and the LMS filter. When the tests had been run all the data was added to data sheets where it could be analyzed and have the filters added to the data. From the gathered data the data spikes were clearly visible and were more than enough to trigger the mower's emergency stop and need to be manually reset. The vibrations were too irregular to filter using the LMS filter since it requires a known signal to filter against. Hence only the complementary filter was implemented fully. With the complementary filter these vibrations can be minimized and brought well below the level required to trigger an emergency stop. With a high filter weight constant such as 0.98, the margin of error from vibrations can be brought down to +- 1 degrees as the lowest and +- 4,6 degrees as highest depending on the surface and automower under testing. The main advantage with using the complementary filter is that it only requires one weight constant to adjust the filter intensity making it easy to use. The one disadvantage is that the higher the weight constant is the more delay there is on the data.
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Орлов, Олександр Олегович. "Аналітичний підхід до наближеного розв’язку задач динаміки гіроскопічних систем." Магістерська робота, 2020. https://dspace.znu.edu.ua/jspui/handle/12345/1982.
Full textAbstract:
Орлов О. О. Аналітичний підхід до наближеного розв’язку задач динаміки гіроскопічних систем : кваліфікаційна робота магістра спеціальності 113 "Прикладна математика" / наук. керівник В. З. Грищак. Запоріжжя : ЗНУ, 2020. 57 с.UA : Робота викладена на 57 сторінках друкованого тексту, містить 15 рисунків, 53 джерела, 1 додаток. Об’єктом дослідження є наближений аналітичний метод аналізу коливань гіроскопічних систем. Мета роботи: застосування сучасних методів дослідження коливань систем, які обертаються, з масою залежною від часу, зокрема наближеного аналітичного підходу на базі асимптотичного методу. Методи дослідження: аналітичний, чисельний. У кваліфікаційній роботі розглядаються коливання конструкцій, маса яких неперіодично залежить від часу. Проаналізовано методи аналізу даних коливань. Наведено приклади основні рівняння вимушених коливань. Показано розрахунок коливання конструкцій методом фазних інтегралів. Проведено чисельний аналіз на базі наближеного аналітичного підходу та чисельний аналіз вимушених коливань гіроскопічних системи з масою залежною від часу. Результати можуть бути використані при викладанні та вивченні курсів математичної фізики та аналізу проблем механіки деформованого твердого тіла.
EN : The work is presented on 57 pages of printed text, 15 figures, 53 references, 1 supplement. The object of the study is an approximate analytical method for the analysis of oscillations of gyroscopic systems. Purpose: to apply modern methods of study of oscillations of rotating systems with time-dependent mass, in particular the approximate analytical approach based on the asymptotic method. Research methods are analytical, numerical. Qualification work deals with fluctuations in structures whose mass is periodically dependent on time. Methods of analysis of data of oscillations are analyzed. Examples of basic equations of forced oscillations are given. The calculation of the oscillation of structures by the method of phase integrals is shown. Numerical analysis is performed on the basis of approximate analytical approach and numerical analysis of forced oscillations of gyroscopic system with time dependent mass. The results can be used to teach and study mathematical physics courses and to analyze the problems of deformed solid mechanics.
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Mousavi, Lajimi Seyed Amir. "Design, Modeling, and Nonlinear Dynamics of a Cantilever Beam-Rigid Body Microgyroscope." Thesis, 2013. http://hdl.handle.net/10012/8060.
Full textAbstract:
A new type of cantilever beam gyroscope is introduced, modeled, and analyzed. The main structure includes a cantilever beam and a rigid body attached to the free end of the beam. The model accounts for the eccentricity, that is the offset of the center of mass of the rigid body relative to the beam's free end. The first and second moments of mass and the rotary inertia appear in the equations of motion and boundary conditions. The common mechanism of electrostatic actuation of microgyroscopes is used with the difference of computing the force at the center of mass resulting in the electrostatic force and moment in the boundary conditions. By using the extended Hamilton's principle, the method of assumed modes, and Lagrange's differential equations, the equations of motion, boundary conditions, and the discretized model are developed. The generalized model simplifies to other beam gyroscope models by setting the required parameters to zero.
Considering the DC and AC components of the actuating and sensing methods, the response is resolved into the static and dynamic components. The static configuration is studied for an increasing DC voltage. For the uncoupled system of equations, the explicit equation relating the DC load and the static configuration is computed and solved for the static configuration of the beam-rigid body in each direction. Including the rotation rate, the stationary analysis is performed, the stationary pull-in voltage is identified, and it is shown that the angular rotation rate does not affect the static configuration. The modal frequencies of the beam-rigid body gyroscope are studied and the instability region due to the rotation rate is computed. It is shown that the gyroscope can operate in the frequency modulation mode and the amplitude modulation mode. To operate the beam-rigid body gyroscope in the frequency modulation mode, the closed-form relation of the observed modal frequency split and the input rotation rate is computed. The calibration curves are generated for a variety of DC loads. It is shown that the scale factor improves by matching the zero rotation rate natural frequencies.
The method of multiple scales is used to study the reduced-order nonlinear dynamics of the oscillations around the static equilibrium. The modulation equations, the ``slow'' system, are derived and solved for the steady-state solutions. The computational shooting method is employed to evaluate the results of the perturbation method. The frequency response and force response plots are generated. For combinations of parameters resulting in a single-valued response, the two methods are in excellent agreement. The synchronization of the response occurs in the sense direction for initially mismatched natural frequencies. The global stability of the system is studied by drawing phase-plane diagrams and long-time integration of response trajectories. The separatrices are computed, the jump phenomena is numerically shown, and the dynamic pull-in of the response is demonstrated. The fold bifurcation points are identified and it is shown that the response jumps to the higher/lower branch beyond the bifurcation points in forward/backward sweep of the amplitude and the excitation frequency of AC voltage.
The mechanical-thermal (thermomechanical) noise effect on the sense response is characterized by using a linear approximation of the system and the nonlinear "slow" system obtained by using the method of multiple scales. To perform linear analysis, the negligible effect of Coriolis force on the drive amplitude is discarded. The second-order drive resonator is solved for the drive amplitude and phase. Finding the sense response due to the thermal noise force and the Coriolis force and equating them computes the mechanical-thermal noise equivalent rotation rate in terms of system parameters and mode shapes. The noise force is included in the third-order equation of the perturbation and equation to account for that in the reduced-order nonlinear response. The numerical results of linear and reduced-order nonlinear thermal noise analyses agree. It is shown that higher quality factor, higher AC voltage, and operating at lower DC points result in better resolution of the microsensor.
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Deng, Jian. "Fractional Stochastic Dynamics in Structural Stability Analysis." Thesis, 2013. http://hdl.handle.net/10012/7816.
Full textAbstract:
The objective of this thesis is to develop a novel methodology of fractional
stochastic dynamics to study stochastic stability of viscoelastic
systems under stochastic loadings.
Numerous structures in civil engineering are driven by dynamic forces, such as
seismic and wind loads, which can be described satisfactorily only by using
probabilistic models, such as white noise processes, real noise processes, or
bounded noise processes. Viscoelastic materials exhibit time-dependent stress
relaxation and creep; it has been shown that fractional calculus provide a
unique and powerful mathematical tool to model such a hereditary property.
Investigation of stochastic stability of viscoelastic systems with fractional
calculus frequently leads to a parametrized family of fractional stochastic
differential equations of motion. Parametric excitation may cause parametric
resonance or instability, which is more dangerous than ordinary resonance as it
is characterized by exponential growth of the response amplitudes even in the
presence of damping.
The Lyapunov exponents and moment Lyapunov exponents provide not only the
information about stability or instability of stochastic systems, but also how
rapidly the response grows or diminishes with time. Lyapunov exponents
characterizes sample stability or instability. However, this sample stability
cannot assure the moment stability. Hence, to obtain a complete picture of the
dynamic stability, it is important to study both the top Lyapunov exponent and
the moment Lyapunov exponent. Unfortunately, it is very difficult to obtain the
accurate values of theses two exponents. One has to resort to numerical and
approximate approaches.
The main contributions of this thesis are: (1) A new numerical simulation
method is proposed to determine moment Lyapunov exponents of fractional
stochastic systems, in which three steps are involved: discretization of
fractional derivatives, numerical solution of the fractional equation, and an
algorithm for calculating Lyapunov exponents from small data sets. (2)
Higher-order stochastic averaging method is developed and applied to
investigate stochastic stability of fractional viscoelastic
single-degree-of-freedom structures under white noise, real noise, or bounded
noise excitation. (3) For two-degree-of-freedom coupled non-gyroscopic and
gyroscopic viscoelastic systems under random excitation, the Stratonovich
equations of motion are set up, and then decoupled into four-dimensional Ito
stochastic differential equations, by making use of the method of stochastic
averaging for the non-viscoelastic terms and the method of Larionov for
viscoelastic terms. An elegant scheme for formulating the eigenvalue problems
is presented by using Khasminskii and Wedig’s mathematical transformations from
the decoupled Ito equations. Moment Lyapunov exponents are approximately
determined by solving the eigenvalue problems through Fourier series expansion.
Stability boundaries, critical excitations, and stability index are obtained.
The effects of various parameters on the stochastic stability of the system are
discussed. Parametric resonances are studied in detail. Approximate analytical
results are confirmed by numerical simulations.